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Minnesota functionals

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Minnesota Functionals (Myz) are a group of approximate exchange-correlation energy functionals in density functional theory (DFT). They are developed by the group of Prof. Donald Truhlar at the University of Minnesota. These functionals are based on the meta-GGA approximation, i.e. they include terms that depend on the kinetic energy density, and are all based on complicated functional forms parametrized on high-quality benchmark databases. These functionals can be used for traditional quantum chemistry and solid-state physics calculations. The Myz functionals are widely used and tested in the quantum chemistry community. Independent evaluations of the strengths and limitations of the Minnesota functionals with respect to various chemical properties have, however, cast doubts on the accuracy of Minnesota functionals. The Minnesota group refutes this criticism claiming that the focus on main-group chemistry or atomic densities in high charge states (such as the Ne8+ ion) is hardly relevant to real applications of density functional theory in computational chemistry.

Contents

Minnesota functionals are available in a large number of popular quantum chemistry computer programs.

Minnesota 05

The first family of Minnesota functionals, published in 2005, is composed by:

  • M05: Global hybrid functional with 28% HF exchange.
  • M05-2X Global hybrid functional with 56% HF exchange.

    • Minnesota 06

    The '06 family represent a general improvement over the 05 family and is composed of:

  • M06-L: Local functional, 0% HF exchange. Intended to be fast, good for transition metals, inorganic and organometallics.
  • M06: Global hybrid functional with 27% HF exchange. Intended for main group thermochemistry and non-covalent interactions, transition metal thermochemistry and organometallics. It is usually the most versatile of the 06 functionals, and because of this large applicability it can be slightly worse than M06-2X for specific properties that require high percentage of HF exchange, such as thermochemistry and kinetics.
  • M06-2X: Global hybrid functional with 54% HF exchange. It is the top performer within the 06 functionals for main group thermochemistry, kinetics and non-covalent interactions, however it cannot be used for cases where multi-reference species are or might be involved, such as transition metal thermochemistry and organometallics.
  • M06-HF: Global hybrid functional with 100% HF exchange. Intended for charge transfer TD-DFT and systems where self-interaction is pathological.

    • Minnesota 08

    The '08 family was created with the primary intent to improve the M06-2X functional form, retaining the performances for main group thermochemistry, kinetics and non-covalent interactions. This family is composed by two functionals with a high percentage of HF exchange, with performances similar to those of M06-2X:

  • M08-HX: Global hybrid functional with 52.23% HF exchange. Intended for main group thermochemistry, kinetics and non-covalent interactions.
  • M08-SO: Global hybrid functional with 56.79% HF exchange. Intended for main group thermochemistry, kinetics and non-covalent interactions.

    • Minnesota 11

    The '11 family introduces range-separation in the Minnesota functionals and modifications in the functional form and in the training databases. These modifications also cut the number of functionals in a complete family from 4 (M06-L, M06, M06-2X and M06-HF) to just 2:

  • M11-L: Local functional (0% HF exchange) with dual-range DFT exchange. Intended to be fast, to be good for transition metals, inorganic, organometallics and non-covalent interactions, and to improve much over M06-L.
  • M11: Range-separated hybrid functional with 42.8% HF exchange in the short-range and 100% in the long-range. Intended for main group thermochemistry, kinetics and non-covalent interactions, with an intended performance comparable to that of M06-2X, and for TD-DFT applications, with an intended performance comparable to M06-HF.

    • Minnesota 12

    The 12 family uses a Nonseparable (MN) functional form aiming to provide balanced performance for both chemistry and solid-state physics applications. It is composed by:

  • MN12-L: A local functional, 0% HF exchange. The aim of the functional was to be very versatile and provide good computational performance and accuracy for energetic and structural problems in both chemistry and solid-state physics.
  • MN12-SX: Screened-exchange (SX) hybrid functional with 25% HF exchange in the short-range and 0% HF exchange in the long-range. MN12-L was intended to be very versatile and provide good performance for energetic and structural problems in both chemistry and solid-state physics, at a computational cost that is intermediate between local and global hybrid functionals.

    • Main Software with Implementation of the Minnesota Functionals

    * Using LibXC.

    References

    Minnesota functionals Wikipedia
    (Text) CC BY-SA